The 18-year-old has broke into the Reds' first-team this term, making seven appearances, and has enjoyed a fine vein of form for both club and country.
Right-back Alexander-Arnold was once again excellent for Keith Downing's men, finding the breakthrough after just nine minutes as he drilled inside the near post.
After Chelsea's Dujon Sterling brought down inside the box in the second-half, Alexander-Arnold converted the spot-kick to make it 2-0 - before Arsenal striker Chris Willock made sure of victory late on.
Liverpool Academy graduate Alexander-Arnold's performance followed a display in which he laid on an assist and played a large part in another as England U19s beat Norway 3-0.
England have now qualified for the finals thanks to their superior head-to-head record against Norway and Spain, the only other nations that can finish level on points with the Young Lions in Group 3.
They round off their elite qualifying campaign on Monday afternoon when they host Belarus - who have lost 5-0 to Spain and 2-1 to Norway so far - in their third match in just five days.
Welsh trio Wilson, Woodburn and Ward watch draw with Ireland from the bench
Elsewhere Liverpool prospects Ben Woodburn and Harry Wilson were both unused substitutes as Wales' only game of the two-week break saw them draw with the Republic of Ireland in a 2018 World Cup qualifier.
The game was marred by Everton right-back Seamus Coleman's leg break, the Irishman having to be stretchered off after he was caught high and late by Neil Taylor - who was sent off.
The result was however a damaging one for Chris Coleman's Wales, who are four points off second-placed Ireland - on 11 points, the same as Serbia - after five games as they look to feature in the World Cup finals for the first time since 1958.
Goalkeeper Danny Ward - currently on loan at Huddersfield Town - was also an unused substitute for Wales, while Joe Gomez, featuring in the England Under-21s squad for the first time since his anterior cruciate ligament injury on international duty in October 2015 - watched his side's 1-0 defeat to Germany from the bench.
Aidy Boothroyd's team continue their preparations for next summer's European Under-21 Championship against Denmark on Monday, when Gomez will hope to get some minutes.